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Statements
W
(
1
2
μ
2
,
μ
t
2
)
∼
2
-
1
2
e
-
1
4
π
μ
2
l
(
μ
)
(
t
2
-
1
)
1
4
(
cos
σ
∑
s
=
0
∞
(
-
1
)
s
𝒜
2
s
(
t
)
μ
4
s
-
sin
σ
∑
s
=
0
∞
(
-
1
)
s
𝒜
2
s
+
1
(
t
)
μ
4
s
+
2
)
,
asymptotic-expansion
parabolic-W
1
2
superscript
𝜇
2
𝜇
𝑡
2
superscript
2
1
2
superscript
𝑒
1
4
𝜋
superscript
𝜇
2
𝑙
𝜇
superscript
superscript
𝑡
2
1
1
4
𝜎
superscript
subscript
𝑠
0
superscript
1
𝑠
subscript
𝒜
2
𝑠
𝑡
superscript
𝜇
4
𝑠
𝜎
superscript
subscript
𝑠
0
superscript
1
𝑠
subscript
𝒜
2
𝑠
1
𝑡
superscript
𝜇
4
𝑠
2
{\displaystyle{\displaystyle W\left(\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right)%
\sim\frac{2^{-\frac{1}{2}}e^{-\frac{1}{4}\pi\mu^{2}}l(\mu)}{(t^{2}-1)^{\frac{1%
}{4}}}\left(\cos\sigma\sum_{s=0}^{\infty}(-1)^{s}\frac{{\cal{A}}_{2s}(t)}{\mu^%
{4s}}-\sin\sigma\sum_{s=0}^{\infty}(-1)^{s}\frac{{\cal{A}}_{2s+1}(t)}{\mu^{4s+%
2}}\right),}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
W
(
a
,
x
)
parabolic-W
𝑎
𝑥
{\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
s
𝑠
{\displaystyle{\displaystyle s}}
𝒜
s
(
t
)
subscript
𝒜
𝑠
𝑡
{\displaystyle{\displaystyle\mathcal{A}_{s}(t)}}
σ
𝜎
{\displaystyle{\displaystyle\sigma}}
l
(
μ
)
𝑙
𝜇
{\displaystyle{\displaystyle l(\mu)}}
Identifiers
